Question

Determine the exact value of cos 135 degrees and explain how you knew to use the side lengths you used

Answer 1

Step-by-step explanation

We are required to determine the exact value of cos 135°.

Since the angle lies in the second quadrant, we have:

`\begin{gathered} \cos135\degree=\cos(180\degree-45\degree) \\ \cos135\degree=-\cos45\degree \end{gathered}`

To determine the value of x, we have:

`\begin{gathered} \text{ Using the Pythagorean theorem,} \\ x^2=1^2+1^2 \\ x=√(1^2+1^2) \\ x=√(1+1) \\ x=√(2) \end{gathered}`

Therefore, the value of cos 135° is:

`\begin{gathered} \text{ We know that }cos\theta=(adj)/(hyp) \\ \therefore\cos135\degree=-\cos45\degree=-(1)/(√(2)) \\ \cos135\degree=-(1)/(√(2))*(√(2))/(√(2)) \\ \cos135\degree=-(√(2))/(2) \end{gathered}`

Hence, the answer is:

The lengths used is the lowest length of sides that can be used.